3GS won't work without charger, battery dead?

[supermario66]

Hello all. My mothers 3GS suddenly stopped working, when I connect it to the computer or wall socket it will only show "connect to itunes". If I try to update it I get "unknown error 21".

I've tried most things, changing the host file, trying different computers, trying another cord and turned off the firewall. I've tried to put it in DFU mode along with shift restore but to no avail but now I've given up and decided it must be the battery. Which is weird since I changed it less than a year ago, maybe it's broken. The screen doesn't show any charging icon or warning sign about the battery, either.

I'd be happy if someone would help, and merry christmas to all!